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Validation of assay methods is based on the use of calibration and validation standards made by accurately weighing predetermined quantities of analytes as required. The experiments are generally carried out on multiple series (usually carried out on different days) on multiple concentration levels with multiple replicates per level and per series.
In order to complete this report, it is recommended to annex the exact drug formula with the reference of each of the raw materials used as well as a complete description of pre-analytical and analytical methods used.
The estimation of the parameters of the calibration curves were obtained from the ordinary least squares method (OLS) using the r stats::lm() function.
When possible various linear regressions were tested:
Considering \(i \in [1;p]\) (series index), \(j \in [1,m]\) (concentration index), \(k\in [1;n]\) (repetition index) and \(x_{i,j,k, calc}\) the \(k\)th back calculated concentration of the \(i\) series \(j\) level (using calibration standards) :
\[ x_{i,j,k, calc} = \mu_j + \alpha_{i,j} + \epsilon_{i,j,k} \]
With : \(\begin{cases} \mu_j &: \text{the back calculated mean of the $j$ level} \\ \alpha_{i,j} &: \text{at $j$ level, the difference between the $i$th series average and the $\mu_j$}\\ \epsilon_{i,j,k} &: \text{the experimental error} \end{cases}\)
\(\begin{cases}\alpha_{i,j} &\sim \mathcal{N}(0,\sigma^2_{B,j}) \; \text{with $\sigma^2_{B,j}$ representing the interseries variances} \\ \epsilon_{i,j,k} &\sim \mathcal{N}(0, \sigma^2_{W,j}) \; \text{with $\sigma^2_{W,j}$ representing the intraseries variances}\end{cases}\)
Trueness expresses the closeness of agreement between the mean value obtained from a series of test results and an accepted reference value. The trueness gives an indication of the systemic errors. It was calculated at each concentration level by calculating the difference between the introduced concentrations (arithmetic) mean \(\overline{x}_j\) and the calculated concentrations mean \(\hat{\mu}_j\).
The bias (for j th level) was expressed as: \(\text{Bias}_j =\hat{\mu}_j-\overline{x}_j\)
And the relative bias as: \(\text{Bias(%)}_j = \frac{\hat{\mu}_j-\overline{x}_j}{\overline{x}_j}\times 100\)
The recovery (for j th level) was expressed as : \(\text{Recovery(%)}_j = \frac{\hat{\mu}_j}{\overline{x}_j}\times 100\)
Fidelity expresses the closeness of agreement between a series of measurements from multiple takes of the same homogeneous sample, under prescribed conditions. It provides information on random errors and is assessed at two levels, repeatability and intermediate precision.
Intra and interseries variance could be estimated at every \(j\) level using the restricted maximum likelihood method:
\(\begin{align} \hat{\mu}_j &= \frac{1}{\sum^p_{i=1}n_{i,j}}\cdot\sum^p_{i=1}\sum^{n_{i,j}}_{k=1} x_{i,j,k, calc} \\ \text{MSM}_j &= \frac{1}{p-1} \cdot \sum^p_{i=1}n_{i,j}\cdot \left(x_{i,j, calc}-\overline{x}_{i,j, calc}\right)^2 \\ \text{MSE}_j &=\frac{1}{\sum^p_{i=1}n_{i,j}-p}\cdot\sum^p_{i=1}\sum^{n_{i,j}}_{k=1} \left(x_{i,j, calc}-\overline{x}_{i,j, calc}\right)^2 \end{align}\)
\(\text{if MSE$_j$ < MSM$_j$} \begin{cases} \hat{\sigma}^2_{W,j} &=\text{MSE}_j \\ \hat{\sigma}^2_{B,j} &= \frac{\text{MSM}_j-\text{MSE}_j}{n} \end{cases}\)
\(\text{else} \begin{cases} \hat{\sigma}^2_{W,j} &=\frac{1}{pn - 1}\cdot\sum^p_{i=1}\sum^{k}_{j=1} \left(x_{i,j,k calc}-\overline{x}_{j, calc}\right)^2 \\ \hat{\sigma}^2_{B,j} &= 0 \end{cases}\)
Intermediate precision was then calculated: \(\hat{\sigma}^2_{IP,j} = \hat{\sigma}^2_{W,j} + \hat{\sigma}^2_{B,j}\)
Each corresponding coefficient of variation was determined as: \(\text{CV(%)} = \frac{\sigma_j}{\hat{\mu}_j}\)
The tolerance interval is a statistical interval within which, with some confidence level, a specified proportion (\(\beta\)) of a sampled population falls. The construction of the tolerance intervals using standard solutions therefore makes it possible to predict with a some confidence levels where a proportion of the dosages will falls.
The tolerance interval has been computed, at each concentration levels using validation standards as follows:
\(\hat{\mu}_j \pm \mathcal{Q}t(\upsilon,\frac{1 + \beta}{2})\cdot\sqrt{1 + \frac{1}{pn\cdot B^2_j}}\cdot\hat\sigma_{IP,j}\)
\(\text{Bias(%)} \pm \mathcal{Q}_t(\upsilon,\frac{1 + \beta}{2}) \cdot \sqrt{1 + \frac{1}{pn\cdot B^2_j}} \cdot \hat{ \text{CV}}_{IP,j}\)
\(with \begin{cases}\begin{align} R_j &= \frac{\sigma^2_{B,j}}{\sigma^2_{W,j}} \\ B_j &= \sqrt{\frac{R_j +1}{n\cdot R_j + 1}} \\ \upsilon &= \frac{(R+1)^2}{\frac{(R + (1/n))^2}{p - 1} + \frac{(1 - 1/n)}{pn} } \end{align}\end{cases}\)
\(\mathcal{Q}_t(\upsilon,\frac{1 + \beta}{2})\) corresponded to the \(\beta\) quantile of the Student \(t\) distribution with \(\upsilon\) degrees of freedom.
The accuracy profiles (â) were plotted joining the tolerance intervals obtained for each of the levels tested. A method is validated over the full range of measurements, when the accuracy profile (â) is fully included between the upper and lower bound of the acceptability limit \([-\lambda;+\lambda]\) (â) set a priori. The method can only be used over the concentration range for which the accuracy profile is entirely within the acceptability limit \([-\lambda;+\lambda]\).
When the accuracy profile (â) is not fully included within the acceptability limit \([-\lambda;+\lambda]\) ( â), a limit of quantification can be determined at the intersection of the accuracy profile with the upper (\(+\lambda\)) or lower (\(-\lambda\)) acceptability limit. This can happen at low or high concentrations and can produce lower or higher LOQs respectively.
The coordinates of the intersections between the accuracy profiles and the acceptability limits were calculated and plotted on the tolerance profiles (â´)
The lower LOQ is the lowest amount of analyte in a sample which can be quantitatively determined with suitable precision and accuracy. It should be determined at lower levels using the last intersection point between accuracy profile and acceptance limits, before accuracy profile become fully included in acceptance limits. Itâs the first level tested if accuracy profile is fully inside acceptance limits at this level.
The upper LOQ is the highest amount of analyte in a sample which can be quantitatively determined with suitable precision and accuracy. It should be determined at higher levels using the first intersection point between accuracy profile and acceptance limits, before accuracy profile partly or fully exceeds acceptance limits. It is the last level tested if accuracy profile is fully inside acceptance limits from the lower LOQ to this level.
Response functions \(signal=f(concentration)\) were analysed using stats4::lm() function in R, using calibration data provided in Table 4.1 and Figure 4.1) (see section 4).
Analysis was performed using :
The interactive table 2.1 shows the values obtained with regressions :
| Methods | Serie | Intercept | Slope | AIC | R² |
|---|---|---|---|---|---|
| Linear (LM) | 1 | -1358.7877 | 7566838 | 188.82847 | 0.9987755 |
| Linear (LM) | 2 | -2972.4758 | 7166164 | 157.35429 | 0.9999733 |
| Linear (LM) | 3 | -4450.9923 | 7101554 | 178.31360 | 0.9996262 |
| Linear 0 (LM) | 1 | 0.0000 | 7559372 | 186.84928 | 0.9991447 |
| Linear 0 (LM) | 2 | 0.0000 | 7149831 | 159.29751 | 0.9999694 |
| Linear 0 (LM) | 3 | 0.0000 | 7077097 | 177.10514 | 0.9997112 |
| Linear 0-max (LM) | 1 | 0.0000 | 7559800 | 52.44744 | 0.9991522 |
| Linear 0-max (LM) | 2 | 0.0000 | 7151585 | 43.89910 | 0.9999868 |
| Linear 0-max (LM) | 3 | 0.0000 | 7083672 | 48.34795 | 0.9998756 |
| Linear weighed 1/X (LM) | 1 | -1461.3560 | 7568686 | 165.82140 | 0.9987859 |
| Linear weighed 1/X (LM) | 2 | -2165.6005 | 7151626 | 156.85434 | 0.9995574 |
| Linear weighed 1/X (LM) | 3 | -530.7419 | 7030919 | 166.86941 | 0.9984005 |
| Linear weighed 1/Y (LM) | 1 | -1687.6258 | 7562968 | 165.13549 | 0.9986793 |
| Linear weighed 1/Y (LM) | 2 | -2215.1444 | 7146698 | 159.77107 | 0.9991691 |
| Linear weighed 1/Y (LM) | 3 | -575.2321 | 7018751 | 167.75477 | 0.9981079 |
The residues obtained are shown in the interactive figure 2.1.
Figure 2.1: Relative bias calculated from regression
Trueness and precision are depicted on table 3.1 and 3.2
| Introduced concentrations default | Mean calculated concentrations default | Bias default | Repeatability SD default | Between series SD default | Intermediate precision SD default | Low limit of tolerance default | High limit of tolerance default |
|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0007239 | 0.0002239 | 0.0001373 | 1.0e-07 | 0.0002666 | 0.0002355 | 0.0012122 |
| 0.0015 | 0.0016881 | 0.0001881 | 0.0002630 | 0.0e+00 | 0.0003053 | 0.0012286 | 0.0021476 |
| 0.0200 | 0.0195866 | -0.0004134 | 0.0014254 | 6.0e-07 | 0.0016220 | 0.0171659 | 0.0220074 |
| 0.2000 | 0.1999305 | -0.0000695 | 0.0114414 | 7.6e-06 | 0.0117702 | 0.1830347 | 0.2168264 |
| Introduced concentrations default | Mean calculated concentrations default | Bias (%) | Recovery (%) | CV repeatability (%) | CV intermediate precision (%) | Low limit of tolerance (%) | High limit of tolerance (%) | Results |
|---|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0007239 | 44.775711 | 144.77571 | 27.459330 | 53.325616 | -52.893662 | 142.445083 | FAIL |
| 0.0015 | 0.0016881 | 12.540253 | 112.54025 | 17.534663 | 20.355825 | -18.092530 | 43.173037 | FAIL |
| 0.0200 | 0.0195866 | -2.066788 | 97.93321 | 7.126778 | 8.109942 | -14.170430 | 10.036855 | FAIL |
| 0.2000 | 0.1999305 | -0.034729 | 99.96527 | 5.720705 | 5.885101 | -8.482649 | 8.413191 | PASS |
Accuracy profile is shown Figure 3.1. The đ˝-tolerance interval (â) should be entirely within the acceptance limits (â). Coordinates of points of intersection between the tolerance interval and the acceptability limit were marked with a red star (â´) when present.
Figure 3.1: Accuracy profiles (red dashed line: acceptance limits, blue lines: đ˝-tolerance intervals).
Linearity profile is shown Figure 3.2. You should check that the black line (linear model) should be superimposed on the red dashed identity line.
Figure 3.2: Linearity profiles (red dashed line: identity line, black lines: linear regression lines, blue lines: đ˝-tolerance intervals).
The p-value for the intercept is > 0.05 which is in favor of a non-significant value (PASS)
The p-value for the slope is < 0.05 which is in favor of a significant value (PASS)
| Estimate | CI (lower) | CI (upper) | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|---|---|
| (Intercept) | 0.0000175 | -0.0019941 | 0.0020292 | 0.0009994 | 0.0175485 | 0.986 | |
| x | 0.9993649 | 0.9793491 | 1.0193808 | 0.0099438 | 100.5013829 | <0.001 | *** |
The p-value < 0.05 which is in favor of heterosedasticity and standard deviations of a calculated concentrations as related to introduced concentrations, are non-constant (this should be investigated)
| Test statistic | df | P value |
|---|---|---|
| 5.044 | 1 | 0.02471 * |
Trueness and precision are depicted on the table 3.4 and 3.5
| Introduced concentrations default | Mean calculated concentrations default | Bias default | Repeatability SD default | Between series SD default | Intermediate precision SD default | Low limit of tolerance default | High limit of tolerance default |
|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0003176 | -0.0001824 | 0.0001376 | 0.0e+00 | 0.0001376 | 0.0001219 | 0.0005133 |
| 0.0015 | 0.0012839 | -0.0002161 | 0.0002636 | 0.0e+00 | 0.0002636 | 0.0009091 | 0.0016587 |
| 0.0200 | 0.0192220 | -0.0007780 | 0.0014294 | 8.0e-07 | 0.0016996 | 0.0166384 | 0.0218056 |
| 0.2000 | 0.1999679 | -0.0000321 | 0.0114542 | 7.5e-06 | 0.0117785 | 0.1830626 | 0.2168732 |
| Introduced concentrations default | Mean calculated concentrations default | Bias (%) | Recovery (%) | CV repeatability (%) | CV intermediate precision (%) | Low limit of tolerance (%) | High limit of tolerance (%) | Results |
|---|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0003176 | -36.4882832 | 63.51172 | 27.525332 | 27.525332 | -75.627610 | 2.651044 | FAIL |
| 0.0015 | 0.0012839 | -14.4058986 | 85.59410 | 17.570893 | 17.570893 | -39.390627 | 10.578829 | FAIL |
| 0.0200 | 0.0192220 | -3.8899655 | 96.11003 | 7.146753 | 8.497997 | -16.808072 | 9.028141 | FAIL |
| 0.2000 | 0.1999679 | -0.0160614 | 99.98394 | 5.727122 | 5.889251 | -8.468712 | 8.436589 | PASS |
Accuracy profile is shown in Figure 3.3. The đ˝-tolerance interval (â) should be entirely within the acceptance limits (â). Coordinates of points of intersection between the tolerance interval and the acceptability limit were marked with a red star (â´) when present.
Figure 3.3: Accuracy profiles (red dashed line: acceptance limits, blue lines: đ˝-tolerance intervals).
Linearity profile is shown in Figure 3.4. You should check that the black line (linear model) should be superimposed on the red dashed identity line.
Figure 3.4: Linearity profiles (red dashed line: identity line, black lines: linear regression lines, blue lines: đ˝-tolerance intervals).
The p-value for the intercept is > 0.05 which is in favor of a non-significant value (PASS)
The p-value for the slope is < 0.05 which is in favor of a significant value (PASS)
| Estimate | CI (lower) | CI (upper) | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|---|---|
| (Intercept) | -0.0003905 | -0.0024046 | 0.0016237 | 0.0010006 | -0.3902287 | 0.698 | |
| x | 1.0015911 | 0.9815504 | 1.0216317 | 0.0099561 | 100.6004122 | <0.001 | *** |
The p-value < 0.05 which is in favor of heterosedasticity and standard deviations of a calculated concentrations as related to introduced concentrations, are non-constant (this should be investigated)
| Test statistic | df | P value |
|---|---|---|
| 5.05 | 1 | 0.02462 * |
Trueness and precision are depicted on the table 3.7 and 3.8
| Introduced concentrations default | Mean calculated concentrations default | Bias default | Repeatability SD default | Between series SD default | Intermediate precision SD default | Low limit of tolerance default | High limit of tolerance default |
|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0003174 | -0.0001826 | 0.0001376 | 0.0e+00 | 0.0001376 | 0.0001218 | 0.0005130 |
| 0.0015 | 0.0012834 | -0.0002166 | 0.0002635 | 0.0e+00 | 0.0002635 | 0.0009088 | 0.0016580 |
| 0.0200 | 0.0192142 | -0.0007858 | 0.0014286 | 9.0e-07 | 0.0017009 | 0.0166273 | 0.0218012 |
| 0.2000 | 0.1998863 | -0.0001137 | 0.0114533 | 7.8e-06 | 0.0117893 | 0.1829597 | 0.2168130 |
| Introduced concentrations default | Mean calculated concentrations default | Bias (%) | Recovery (%) | CV repeatability (%) | CV intermediate precision (%) | Low limit of tolerance (%) | High limit of tolerance (%) | Results |
|---|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0003174 | -36.5154449 | 63.48456 | 27.511253 | 27.511253 | -75.634752 | 2.603862 | FAIL |
| 0.0015 | 0.0012834 | -14.4401297 | 85.55987 | 17.563399 | 17.563399 | -39.414202 | 10.533942 | FAIL |
| 0.0200 | 0.0192142 | -3.9288280 | 96.07117 | 7.142830 | 8.504340 | -16.863670 | 9.006014 | FAIL |
| 0.2000 | 0.1998863 | -0.0568324 | 99.94317 | 5.726666 | 5.894633 | -8.520142 | 8.406478 | PASS |
Accuracy profile is shown in Figure 3.5. The đ˝-tolerance interval (â) should be entirely within the acceptance limits (â). Coordinates of points of intersection between the tolerance interval and the acceptability limit were marked with a red star (â´) when present.
Figure 3.5: Accuracy profiles (red dashed line: acceptance limits, blue lines: đ˝-tolerance intervals).
Linearity profile is shown in Figure 3.6. You should check that the black line (linear model) should be superimposed on the red dashed identity line.
Figure 3.6: Linearity profiles (red dashed line: identity line, black lines: linear regression lines, blue lines: đ˝-tolerance intervals).
The p-value for the intercept is > 0.05 which is in favor of a non-significant value (PASS)
The p-value for the slope is < 0.05 which is in favor of a significant value (PASS)
| Estimate | CI (lower) | CI (upper) | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|---|---|
| (Intercept) | -0.0003903 | -0.0024057 | 0.0016251 | 0.0010013 | -0.3897947 | 0.698 | |
| x | 1.0011826 | 0.9811289 | 1.0212362 | 0.0099626 | 100.4942902 | <0.001 | *** |
The p-value < 0.05 which is in favor of heterosedasticity and standard deviations of a calculated concentrations as related to introduced concentrations, are non-constant (this should be investigated)
| Test statistic | df | P value |
|---|---|---|
| 5.025 | 1 | 0.02498 * |
Trueness and precision are depicted on the table 3.10 and 3.11
| Introduced concentrations default | Mean calculated concentrations default | Bias default | Repeatability SD default | Between series SD default | Intermediate precision SD default | Low limit of tolerance default | High limit of tolerance default |
|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0005235 | 0.0000235 | 0.0001382 | 0.0e+00 | 0.0001529 | 0.0002980 | 0.0007490 |
| 0.0015 | 0.0014923 | -0.0000077 | 0.0002644 | 0.0e+00 | 0.0002845 | 0.0010772 | 0.0019074 |
| 0.0200 | 0.0194793 | -0.0005207 | 0.0014350 | 7.0e-07 | 0.0016692 | 0.0169653 | 0.0219933 |
| 0.2000 | 0.2007220 | 0.0007220 | 0.0114504 | 6.3e-06 | 0.0117212 | 0.1839255 | 0.2175185 |
| Introduced concentrations default | Mean calculated concentrations default | Bias (%) | Recovery (%) | CV repeatability (%) | CV intermediate precision (%) | Low limit of tolerance (%) | High limit of tolerance (%) | Results |
|---|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0005235 | 4.7026406 | 104.70264 | 27.634133 | 30.571414 | -40.402985 | 49.808267 | FAIL |
| 0.0015 | 0.0014923 | -0.5119997 | 99.48800 | 17.627489 | 18.963577 | -28.185581 | 27.161582 | FAIL |
| 0.0200 | 0.0194793 | -2.6034781 | 97.39652 | 7.174993 | 8.346037 | -15.173646 | 9.966690 | FAIL |
| 0.2000 | 0.2007220 | 0.3609959 | 100.36100 | 5.725221 | 5.860588 | -8.037274 | 8.759265 | PASS |
Accuracy profile is shown in Figure 3.7. The đ˝-tolerance interval (â) should be entirely within the acceptance limits (â). Coordinates of points of intersection between the tolerance interval and the acceptability limit were marked with a red star (â´) when present.
Figure 3.7: Accuracy profiles (red dashed line: acceptance limits, blue lines: đ˝-tolerance intervals).
Linearity profile is shown in Figure 3.8. You should check that the black line (linear model) should be superimposed on the red dashed identity line.
Figure 3.8: Linearity profiles (red dashed line: identity line, black lines: linear regression lines, blue lines: đ˝-tolerance intervals).
The p-value for the intercept is > 0.05 which is in favor of a non-significant value (PASS)
The p-value for the slope is < 0.05 which is in favor of a significant value (PASS)
| Estimate | CI (lower) | CI (upper) | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|---|---|
| (Intercept) | -0.0001867 | -0.0021933 | 0.0018199 | 0.0009969 | -0.187296 | 0.852 | |
| x | 1.0043421 | 0.9843767 | 1.0243076 | 0.0099188 | 101.256809 | <0.001 | *** |
The p-value < 0.05 which is in favor of heterosedasticity and standard deviations of a calculated concentrations as related to introduced concentrations, are non-constant (this should be investigated)
| Test statistic | df | P value |
|---|---|---|
| 5.346 | 1 | 0.02078 * |
Trueness and precision are depicted on the table 3.13 and 3.14
| Introduced concentrations default | Mean calculated concentrations default | Bias default | Repeatability SD default | Between series SD default | Intermediate precision SD default | Low limit of tolerance default | High limit of tolerance default |
|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0005086 | 0.0000086 | 0.0001380 | 0.0e+00 | 0.0001526 | 0.0002835 | 0.0007337 |
| 0.0015 | 0.0014764 | -0.0000236 | 0.0002641 | 0.0e+00 | 0.0002842 | 0.0010615 | 0.0018913 |
| 0.0200 | 0.0194443 | -0.0005557 | 0.0014333 | 7.0e-07 | 0.0016599 | 0.0169489 | 0.0219398 |
| 0.2000 | 0.2004948 | 0.0004948 | 0.0114418 | 5.9e-06 | 0.0116970 | 0.1837403 | 0.2172492 |
| Introduced concentrations default | Mean calculated concentrations default | Bias (%) | Recovery (%) | CV repeatability (%) | CV intermediate precision (%) | Low limit of tolerance (%) | High limit of tolerance (%) | Results |
|---|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0005086 | 1.7219357 | 101.72194 | 27.600381 | 30.520939 | -43.301462 | 46.745333 | FAIL |
| 0.0015 | 0.0014764 | -1.5721901 | 98.42781 | 17.607017 | 18.949962 | -29.230626 | 26.086246 | FAIL |
| 0.0200 | 0.0194443 | -2.7783341 | 97.22167 | 7.166691 | 8.299697 | -15.255678 | 9.699010 | FAIL |
| 0.2000 | 0.2004948 | 0.2473866 | 100.24739 | 5.720891 | 5.848517 | -8.129828 | 8.624601 | PASS |
Accuracy profile is shown in Figure 3.9. The đ˝-tolerance interval (â) should be entirely within the acceptance limits (â). Coordinates of points of intersection between the tolerance interval and the acceptability limit were marked with a red star (â´) when present.
Figure 3.9: Accuracy profiles (red dashed line: acceptance limits, blue lines: đ˝-tolerance intervals).
Linearity profile is shown in Figure 3.10. You should check that the black line (linear model) should be superimposed on the red dashed identity line.
Figure 3.10: Linearity profiles (red dashed line: identity line, black lines: linear regression lines, blue lines: đ˝-tolerance intervals).
The p-value for the intercept is > 0.05 which is in favor of a non-significant value (PASS)
The p-value for the slope is < 0.05 which is in favor of a significant value (PASS)
| Estimate | CI (lower) | CI (upper) | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|---|---|
| (Intercept) | -0.0002008 | -0.0022039 | 0.0018022 | 0.0009951 | -0.2018264 | 0.841 | |
| x | 1.0032769 | 0.9833468 | 1.0232071 | 0.0099012 | 101.3285576 | <0.001 | *** |
The p-value < 0.05 which is in favor of heterosedasticity and standard deviations of a calculated concentrations as related to introduced concentrations, are non-constant (this should be investigated)
| Test statistic | df | P value |
|---|---|---|
| 5.3 | 1 | 0.02132 * |
User provided.
| ID | TYPE | SERIE | SIGNAL | CONC_LEVEL |
|---|---|---|---|---|
| CAL | CAL | 1 | 3057 | 0.00049 |
| CAL | CAL | 1 | 11600 | 0.00150 |
| CAL | CAL | 1 | 155620 | 0.02000 |
| CAL | CAL | 1 | 1556003 | 0.20000 |
| CAL | CAL | 1 | 1720 | 0.00050 |
| CAL | CAL | 1 | 7430 | 0.00150 |
| CAL | CAL | 1 | 145383 | 0.02000 |
| CAL | CAL | 1 | 1467917 | 0.20000 |
| CAL | CAL | 2 | 2144 | 0.00050 |
| CAL | CAL | 2 | 5250 | 0.00150 |
| CAL | CAL | 2 | 142242 | 0.02000 |
| CAL | CAL | 2 | 1425120 | 0.20000 |
| CAL | CAL | 2 | 1847 | 0.00050 |
| CAL | CAL | 2 | 8487 | 0.00150 |
| CAL | CAL | 2 | 137393 | 0.02000 |
| CAL | CAL | 2 | 1435514 | 0.20000 |
| CAL | CAL | 3 | 2744 | 0.00050 |
| CAL | CAL | 3 | 10473 | 0.00150 |
| CAL | CAL | 3 | 141074 | 0.02000 |
| CAL | CAL | 3 | 1400930 | 0.20000 |
| CAL | CAL | 3 | 3422 | 0.00050 |
| CAL | CAL | 3 | 10554 | 0.00150 |
| CAL | CAL | 3 | 115746 | 0.02000 |
| CAL | CAL | 3 | 1432539 | 0.20000 |
Figure 4.1: Calibration data
| ID | TYPE | SERIE | SIGNAL | CONC_LEVEL |
|---|---|---|---|---|
| VAL | VAL | 1 | 1544 | 0.0005 |
| VAL | VAL | 1 | 9992 | 0.0015 |
| VAL | VAL | 1 | 155683 | 0.0200 |
| VAL | VAL | 1 | 1767753 | 0.2000 |
| VAL | VAL | 1 | 1422 | 0.0005 |
| VAL | VAL | 1 | 11212 | 0.0015 |
| VAL | VAL | 1 | 154877 | 0.0200 |
| VAL | VAL | 1 | 1540288 | 0.2000 |
| VAL | VAL | 1 | 3661 | 0.0005 |
| VAL | VAL | 1 | 11527 | 0.0015 |
| VAL | VAL | 1 | 154062 | 0.0200 |
| VAL | VAL | 1 | 1466979 | 0.2000 |
| VAL | VAL | 1 | 2712 | 0.0005 |
| VAL | VAL | 1 | 6007 | 0.0015 |
| VAL | VAL | 1 | 153763 | 0.0200 |
| VAL | VAL | 1 | 1466715 | 0.2000 |
| VAL | VAL | 2 | 2593 | 0.0005 |
| VAL | VAL | 2 | 10558 | 0.0015 |
| VAL | VAL | 2 | 140350 | 0.0200 |
| VAL | VAL | 2 | 1413294 | 0.2000 |
| VAL | VAL | 2 | 2880 | 0.0005 |
| VAL | VAL | 2 | 9174 | 0.0015 |
| VAL | VAL | 2 | 110853 | 0.0200 |
| VAL | VAL | 2 | 1425878 | 0.2000 |
| VAL | VAL | 2 | 1316 | 0.0005 |
| VAL | VAL | 2 | 9065 | 0.0015 |
| VAL | VAL | 2 | 136750 | 0.0200 |
| VAL | VAL | 2 | 1368431 | 0.2000 |
| VAL | VAL | 2 | 1908 | 0.0005 |
| VAL | VAL | 2 | 9657 | 0.0015 |
| VAL | VAL | 2 | 130685 | 0.0200 |
| VAL | VAL | 2 | 1332873 | 0.2000 |
| VAL | VAL | 3 | 1498 | 0.0005 |
| VAL | VAL | 3 | 7730 | 0.0015 |
| VAL | VAL | 3 | 142770 | 0.0200 |
| VAL | VAL | 3 | 1430404 | 0.2000 |
| VAL | VAL | 3 | 3415 | 0.0005 |
| VAL | VAL | 3 | 10179 | 0.0015 |
| VAL | VAL | 3 | 141127 | 0.0200 |
| VAL | VAL | 3 | 1409384 | 0.2000 |
| VAL | VAL | 3 | 3423 | 0.0005 |
| VAL | VAL | 3 | 10600 | 0.0015 |
| VAL | VAL | 3 | 138551 | 0.0200 |
| VAL | VAL | 3 | 1403500 | 0.2000 |
| VAL | VAL | 3 | 1281 | 0.0005 |
| VAL | VAL | 3 | 6198 | 0.0015 |
| VAL | VAL | 3 | 117689 | 0.0200 |
| VAL | VAL | 3 | 1411380 | 0.2000 |
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